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and I doubt whether a single one ever saw the real plant. There were certainly no plants in the room, and no instructions were given for procuring them.” Nor is Prof. Bolton alone in his opinion. Prof. Russell wrote on another occasion (School Review, Jan., 1897): “While in theory each pupil is expected to have in his hands a specimen of all the common plants as they are discussed in class, I have seen the pea studied by a class of thirty boys from a model that never left the teacher's desk during the hour, and at the close of the lesson not a word was said about noting the plant in its cultivated state, although acres of it were growing within a mile of the site; but, on the contrary, the home task assigned was to copy the drawing given in the text-book. I still have my doubts whether the majority of the class did not conceive of the true flower as being about a foot in diameter."

The Law relating to Schools and Teachers. By T. A. Organ, B.A., Barrister-at-Law. xvi. +566 pp. (Leeds : Arnold and Son.) 8s. 64. net.—This volume deals, in an able and exhaus. tive manner, with every phase of the law regulating all classes of schools. The fact that the author is Standing Counsel of the National Union of Teachers is guarantee enough of his perfect familiarity with his subject so far as public elementary schools are concerned ; and we may remind readers of the helpful articles contributed by Mr. Organ to The School World last year as sufficient proof that any difficulties likely to be experienced in secondary schools will be much simplified when treated by the author of this excellent manual. As regards the scope of the treatise, we may say that the whole of the Acts, Minutes, and Regulations which have been issued for the guidance of education are codified, and all recent legislation, up to the rising of Parliament last year, is included. As being of particular interest to teachers in schools other than elementary, it may be stated that separate chapters on “Technical Instruction in England,” “ Intermediate or Secondary Education in Wales,” and “The Teachers' Tenure of Office,” are included. Every teacher and all governors of schools should have a copy of this indispensable guide.

Wilderness Ways. By William J. Long. Second Series. 154 pp. (Edward Arnold. ) ---It is not long ago that we had the opportunity of writing enthusiastically of the first series of Mr. Long's sketches of animal life. The present volume is of the same delightful nature as its predecessor. The youngster who has the good fortune to be introduced to the beasts of the field by Mr. Long will be sure to get to love most of them and to understand them all. Teachers of nature-study cannot afford to neglect these books.

Macmillan's Brushwork Copy-Books. By A. R. Cartwright and F. C. Proctor. Nos. I to 4, 4d. ; and 5 and 6, 5d. — These

5 brushwork copy-books should create a great demand in schools of every grade in which art teaching is recognised as part of the system of education. They form a graduated scheme of lessons commencing with simple brush-forms, and passing on to conventional designs, natural plant-forms, free brush-forms, and brushwork design. Brushwork forms an excellent training in the art of seeing. Its object is twofold. It trains the eye for colour, and creates an appreciation for symmetry and form. The authors are to be commended for having gone to nature for their illustrations. All boys and girls would feel the benefit of hand and eye training such as these books give. The copies are printed on good stout cartridge paper, and seeing the price, should have a large sale.

Sewing and Knitting Diagrams. By E. Hughes. (W. and A. K. Johnston.) Size 34 x 28 in. 35. 6d. each, on cloth and rollers, varnished.-A very comprehensive interpretation of the needlework of Standards I. to VII., as required by the Needlework Schedule of the Education Code, is set forth

in Miss Hughes' seven sheets of diagrams. From the elementary to the more complicated work the diagrams of the specimens are accurate and clear. Moreover, the illustrations are not confined to finished specimens. Method of arranging and tacking, position of the needle and cotton, fastenings on and off, &c., &c., have not been forgotten. The specimens of patching, darning and knitting may be remarked upon as particularly good. Some illustrations of cutting out are given, but in such a set of diagrams these are necessarily somewhat small. The lines are, however, clearly marked, and the spaces on the lined paper are well defined. An excellent little handbook accom. panies the diagrams. This gives practical notes under headings for every lesson required for each standard, and in itself will prove a boon to the teacher of needlework.

Cookery Diagrams. By Hester Davies. (W. & A. K. Johnston.) Size 34 x 28 in. 35. 6d. each, on cloth and rollers, varnished.—These comprise a very interesting and useful set of diagrams compiled by Miss Davies, superintendent of the Cardiff School of Cookery. The variety of methods of cutting up the ox and the sheep adopted in England and in Scotland are very clearly illustrated in Diagram I. No. II. shows the joints most suitable for cooking by boiling, and on the same sheet appear poultry and rabbits trussed for boiling. No. III. is devoted to roasting and baking, and joints of beef, veal, mutton and pork, together with some well-trussed poultry, are shown. No. IV. illustrates stewing, srying and grilling. Nos. V. and VI. show fish and vegetables of various kinds. On each sheet short explanatory notes and hints on cooking are given. The colouring of the diagrams is good and the general style is attractive. This set of diagrams should prove of real value as an aid to teaching cookery in elementary schools. They will doubtless also find a place in every school for training students for cookery diplomas.

The Child's Song and Game Book. By H. K. Moore, Mus. Bac., B.A. 20 pp. (Swan Sonnenschein.) 15.—This further collection of original songs and games for children maintains the high standard of Mr. Moore's previous work. The words and tunes will both appeal to children, with whom this author and composer has long been a favourite.

Thoughts in many Minds on Animal Life. Gathered by H. C. F. 50 pp. (Women's Printing Society.) is. Contains a collection of quotations on the subjects of kindness to animals and the mystery of life. Even at the risk of repetition it would have been better to have given the source of each selection immediately after it. The booklet may form a convenient substitute for Christmas cards or similar purposes.

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The Perfect Composition Roll and Inks. Manufactured by H. J. Herbert and Co., 9, Hamilton Street, Sydney, N.S.W. 125.—This convenient hectograph, the newest form in use in England, has been lately introduced from Australia, where it already enjoys a wide popularity. It has been adopted by the New South Wales and other Colonial Governments, and is in general use amongst schoolmasters, clergymen, banking institutions, and other commercial firms in the colonies. For this reason alone it merits attention. Our trial of the apparatus has proved it to be simple, clean, and effective. As with the ordinary hectograph, the original is written with special inks-black, violet, red or green-but these flow readily, and do not clog the pen. The usual tray of gelatine is, however, replaced by a roll of specially gelatanised paper. The original copy is placed face downwards on the paper, and after an interval of a minute or so is removed ; copies may be produced immediately by applying paper to the surface and rubbing, as was done with the original. Over a hundred clear impressions can easily be obtained, and after a sufficient number of copies has been reproduced the portion of the surface just employed is rolled up towards the unused portion of the roll. Each roll is six yards long, so that after one use it is immediately ready for a second. The surface can be utilised from end to end three times over, and in this way over fifty different papers can be copied by means of one roll of gelatinised paper ; this, at the cost per roll, is not expensive. The apparatus will specially commend itself, we are sure, to teachers who have to set papers in such subjects as shorthand, music and drawing, when the management of a stylographic pen in producing lines of different thickness is confessedly difficult and unsatisfactory. The great merits of “The Composition Roll” are its cleanliness and its immediate readiness for further use.

CORRESPONDENCE.

The Editors do not hold themselves responsible for the opinions

expressed in letters which appear in these columns. As a rule, a letter criticising any article or review printed in THE SCHOOL WORLD will be submitted to the contributor before publication, so that the criticism and reply may appear together.

A Teacher's Library of Classics.

MR. Rouse seems to know so much about classical books, and to be so enthusiastic in spreading the knowledge of them, that I venture to ask if he would be so good as to give some advice to a somewhat different class of readers from that for which he wrote last month. I need not sketch my circumstances. My friend, Mr. H. G. Wells, has told my story in a well-known book. Like many other masters in the smaller secondary schools, I had to begin to teach almost before I had begun to learn. My studies have been mainly in natural science ; I have looked at classics only just so far as was neces. sary to secure a pass in examinations, and the editions which I have used have not cost anything like eighteen shillings each, and have been expressly designed to enable their users lo dispense with many of the books which Mr. Rouse considers indispensable. It is quite possible, I think, that, though Mr. Rouse's knowledge of classical books is so extensive, he is not acquainted with those from which exclusively I have obtained what knowledge of the classics I

possess. Now I have to teach classics, and I want to do it decently; but I have practically no books, and my income is so small that I doubt whether I shall be able to spend in ten years on all kinds of books as much as Mr. Rouse assumes that his readers will be willing to spend on classics alone at a single burst. There are, I suppose, many more teachers, men and women, in my position than in the position of affluence which Mr. Rouse takes for granted. Would he kindly select for us about £ 5 worth of the most necessary classical books, starting from nothing? I do not mean small grammars and cheap editions such as my boys use, nor costly bouks which ought to be in the school library, but books which the teacher needs to have at his elbow.

There are many large grammars, dictionaries and histories. I shall certainly be unable to get them all, but I might get one of each if I was assured that it was the best, i.e., the most likely to help practical teachers. Probably those which Mr. Rouse first takes down from his shelves would be the ones which would suit me best. I always get books second-hand if I possibly can, but that practice sometimes lets me in for a worthless book. I should be grateful if Mr. Rouse could warn me against any such pitfalls with regard to the books which he names—if he cares to give me this help I venture to ask on behalf of many of your readers. For instance, in a recent remainder catalogue I find a Pictorial Atlas of Homer by Professor Anderson,

originally published at 1os. 6d., is on sale for 45. Should I be well advised in buying this instead of the guinea edition which Mr. Rouse mentions?

F. LEWISHAM. Clapham.

I have noted below a few titles of good books which I hope Mr. Lewisham may find useful. If he would care for any titles of good editions of authors, I will send him a few. If I were Mr. Lewisham, I should get complete texts of as many authors as possible. Thus all the dramatists in the “Poetæ Scenici Graeci” can be got for 7s. 6d. or ios. second-hand, and all the chief Latin poets in Weber's “Corpus Poetarum Latinarum," or Postgate's new Corpus,” which costs more but is worth it. Then I should get the best edition possible of one part of each author and work up the rest without notes. The German texts are the cheapest, but they are generally badly printed and their merit is uneven ; the new Oxford series is better but dearer ; the old series of Oxford and Cambridge texts are not reliable.

In conclusion, let me congratulate Mr. Lewisham, who, if his biographer told the truth, has a pearl of great price which outweighs all the dictionaries ever published. Rugby.

W. 11. D. Rouse. DICTIONARIES.

Liddell & Scott Greek Lexicon (8th edition, published kl 16s.); but the 6th edition is almost as useful, and can be got cheap second-hand. (The intermediate edition is hardly more useful than the very small one.) Lewis & Short's Latin Dict. (245.) can also be obtained second hand. Both indispensable for any but elementary work. Smith's Intermediate Classical Dictionary, 18s., is excellent: it deals with Biography, Mythology, and Geography. This, as also Seyffert's Dictionary of Antiquities, can be got second-hand

for about 7s. 6d. GRAMMARS.

Goodwin's Greek Moods and Tenses, second edition (not the first, which is inferior), 145. ; Goodwin's Greek Grammar (6s.), and his Greek Grammar for schools, containing accidence as well (35. 6d.). Kennedy's Latin Grammar (not the primer) will probably be most useful for ordinary work; Roby's Latin Grammar for reference or Roby's School Latin

Grammar ; Lindsay's Short Historical Latin Grammar. HISTORY.

In a convenient size, Oman's (45. 6d.) or Bury's Greek History (8s. 6d.): Liddell's Roman (7s. 6d.), Bury's Early Empire (7s.6d.), and Smith's Gibbon (1os.); all three in

Smith's series. LITERARY.

Moulton's Ancient Classical Drama is designed specially for those not familiar with Greek, and it is a good book.

The pictorial Atlas to Homer is different from the Atlas of Classical Antiquities, and quite worth getting.

The Oral Teaching of Latin. Now that so many of our teachers have seen fit to adopt "direct" and oral methods for the teaching of modern languages, it may be of interest to many to know how far the same methods may be applied to the teaching of Latin and what results can be obtained from their employment. It is hardly necessary to remark that there is not the same prima facie logical necessity for teaching Latin by the use of questions asked and answers given in that language as there is in the case of French and German. There is no such essential importance attached to the power of fluent expression in a lan. guage which is nowhere spoken. Nevertheless, it is possible, as I will endeavour to explain, by the use of such a method to impart to beginners the following desirable possessions, which are briefly :-(a) a good and rapidly acquired vocabulary; (6) a grasp of grammatical construction ; (c) a power of accuracy in

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reading and pronouncing Latin; (1) an intelligent interest in the work of the pupils which cannot otherwise be easily stimulated.

Provided that the material be elementary, the method may be applied to any of the well-known text-books in general use. Let us take as our material the following sentences from Rivington's " Latin Reader, First Term, Book I.” The pupils are supposed to know thoroughly the first three declensions of nouns, adjectives of three and of two terminations, the indicative tenses of active verbs of all four conjugations, and of the verb “sum.” The teacher begins by reading the first sentence, keeping the word groups together thus :-

"Sagitta acris, fortem militem—vulneravit.”

The pupils then repeat the sentence in chorus, keeping the same word-groups until it is read by all to the teacher's satisfac. tion. It is then translated by one of the class. Questions are then asked in the following order :

Subject question :-“Quid fortem militem vulneravit ?”
Object question :-“Quem acris sagitta vulneravit ?"
Predicate question ;-“Quid acris sagitta fecit?”
Enlargement of subject :-"Qualis sagitta militem vulneravit ?"
Enlargement of object :-—"Qualem militem sagitta vulneravit?"

The pupils are asked to place the emphatic word first in their answers, which will be :-(1) “Sagitta militem vulneravit.” (2) "Militem sagitta vulneravit.” (3) Vulneravit militem" or “ Vulneravit militem sagitta.” (4) “Acris sagitta militem vulneravit.” (5) Fortein militem sagitta vulneravit.”

After the questions have been asked and answered by the class as a whole and by individuals, the next sentence is taken up and treated in the same way.

“Filia tua- carmen cantat.' The questions will be :Quis carmen

cantat ?"

(2) “ Quid filia cantat ?" (3) “Quid facit lilia ?" (4) “Cujus filia cantat ?"

After a sufficient number of sentences have been tho. roughly dealt with, the text-books, which had hitherto been open and freely used, are shut and the questions are asked again, first in sequence and then out of sequence. Two of the pupils are stationed at the blackboard, one to write down the questions as the teacher asks them and the other to write the answers. This familiarises the pupils with the written form of the words. Meanwhile the attention of the rest of the class is diverted from the two pupils at the blackboard by the teacher, who intersperses, with the Latin questions, questions in English on the parsing of words that occur in the material. This is done partly to give the pupils time to write down questions and answers, and partly, of course, for the purpose of drilling the boys in their declensions and conjugations. When sufficient questions have been asked, the attention of the class is directed to the blackboard, and the work of the two writers is corrected by them. Then the text-book is once more opened, and the pupils read a sentence in Latin and translate it into English. This terminates the lesson.

To revert once more to the advantages previously mentioned. The constant practice of answering questions in Latin cannot fail to impress the meaning and form of the words on the pupil's memory. It is wonderful how boys who, no matter how many vocabularies they have learnt by heart, are always at a loss for a Latin word, soon acquire a complete mastery over words and sentences which they have learned in this way. Moreover, the questions seem to have a stimulating effect on some of the bitherto dull and lazy boys. Some previously hopeless duffers, after a few days of this treatment, brighten up wonderfully, and, moreover, the power of accurate reading is quickly cultivated, such blunders as “consilium” for “consulum,” “filis” for “filiis” being quickly eradicated. Finally, it is undeniable that the habitually idle pupils are stimulated by this method to

participate with interest in the work of the class, and the teacher can feel after each Latin "period” that he has really taught at least 99 per cent. of his form something.

W. G. HARTOG. High School, Liverpool Institute.

All Numbers are Equal. It is a grievous misfortune that the late Professor de Morgan is no longer with us to act as the historian of paradoxers, for surely a rigid proof that all numbers are equal is a paradox after his own heart.

The proof of this startling proposition is based, like all mathematical demonstrations, on axioms and definitions. The definition on which the demonstration immediately rests is given by De Morgan in these words : “What is 7 times 3? It is a number which has a 3 for every unit which there is in 7. The direction then is, substitute 3 for i in the formation of 7." (“ Trigonometry and Double Algebra,” London, 1849, page 115.)

The definition has been adopted extensively by recent authors of text-books on arithmetic and algebra under the name of the general definition of multiplication ; it is given in Charles Smith's very excellent “ Treatise on Algebra”; I have seen it in a very admirable series of Swedish text-books; it has now crossed the Atlantic, and, in spite of our very stringent immigration laws, has effected a landing, and has appeared in a number of our recent text-books. In an American School Algebra, bearing the date 1900, the following general definition of multiplication is given : “Multiplication is the process of finding the product from the multiplicand in the same manner as the multiplier is formed from unity.” This is practically identical with De Morgan's definition. Let us now apply it to a few examples and note the result. The formation of 3 from unity is exhibited by the equation

IX3=1+1+1. (1) Therefore to multiply 2 by 3 we have only to substitute 2 for i in equation (1); thus

2x3=2+2+2=6. Again, the formation of 13 from unity is shown in the equation

IXN3= Ni+1+1. (2) To multiply 2 by J3 we must substitute 2 for i in equation (2); hence

2X N3= 12+2+2= . But the formation of 13 from unity may be effected in the manner shown in any of the following equations :

IX 3 = V12+13+1, (3)
IX 13= 1+1+', (4)

IX 13= V1"+1"+1". (5) From equation (3) we get 2 x 13= N 2° +2° +2° = N12; from (4) we get 2 X 13 123 + 2x + 2) = N24; and from (5) 2x N3= 12" +2" +2" = 12" * 3. Comparing the results we have

N/6= 12=24= 2* x 3, whence 6=12=24=2" X 3. Q.E.D.

I am perfectly well aware that an ingenious mathematician can construct a defence of this general definition, and can frame an interpretation of the phrase "in the same manner as the multiplier is formed from unity” that will meet the requirements of the case. But a definition should, like Cæsar's wife, be above suspicion; it should require no defence, and it should be intelligible without an artificial and forced interpretation.

This general definition finds favour with authors and teachers because it furnishes such an easy way of establishing the rules

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for multiplying fractions and for multiplying algebraic numbers. But surely a protest is called for when so vague, ambiguous, and misleading a definition is found in some of the very best of the text-books.

GEORGE M. C. Robson. Scranton, Penn., U.S.A.

November 17th, 1900.

ciphers. The rules finally arrived at and dictated to the pupils are these :

Rules for Whole Numbers and Decimals. 1.-Ciphers are used to represent empty places (not other. wise indicated) between two figures, as in 3002, or between a figure and the decimal point, as in 7400 and .0047. (The point is often invisible.)

II. --Addition and Subtraction. Keep the points in a vertical line.

III.-Multiplication and Division by powers of Ten; see (2) above.

IV.-Multiplication. Put the unit figure of the multiplier under the last of the multiplicand, Ex. (a) 4:56 (6) 6-456 (c) 456

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An Aid to the Teaching of Decimals. In the December number of The School World we were informed by Dr. Bryan, in his valuable article on Common Examination Errors," that “the chief mistakes in answers to arithmetic occur in connection with decimals." He drew special attention to the use of clumsy fractions in preference to decimals and to the frequency of errors in “

fixing the decimal point in products and quotients.” I cannot but hope, therefore, that some teachers will be glad to hear of a simple little device that has proved successful in making decimals not merely intelligible but attractive.

I ought perhaps to premise that my pupils are girls, of from eleven to eighteen years of age. They generally come to me at fourteen, having just “finished decimals.” A few test examples, however, invariably result in such questions as—“ Please, what do you do with the point ?" or, “Do you count the whole numbers as well as the decimals to find where the point goes in the answer?"

My apparatus consists of a few strips of thick cardboard, three inches wide and of various lengths up to two feet; these are divided into three-inch squares, some of which are filled with bold figures. Using a long strip for ruler, I divide the

22.8

661.2 (6) 20= 10 X2 .. we move all the figures one place up

and multiply by 2. (c) ·2= jó :: we move all the figures one place down

and multiply by 2. V.-Division by a Whole Number, Put the decimal point in the quotient as soon as that in the dividend is reached.

Rule for Decimals. Division by a Decimal. Work on this model :3 01495.073= 073

=41.3 No more rules need, I think, be given except on recurring decimals. To show the method for converting a fraction to a decimal I compare the working out of such an expression as £.

I might add that the pupils are never allowed to put down an unnecessary cipher, or to talk about moving the point, or to give the rule for multiplying by ten as “ Add on a cipher."

MARGARET M. MACK. Brighton, December roth, 1900.

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blackboard in vertical columns, heading them Units, Tens, Hundreds, &c., and (after the first lesson) Tenths, Hundreths, &c. Before producing my strips I make the pupils compare the Roman and Arabic systems of notation, that they may rediscover the principle of local value and also the absence of a Roman symbol answering to the cipher. The question then arises, “ What is the use of ciphers ?" and I show that by putting the figures in named columns they could be dispensed with. The strips are slipped backwards and forwards in the grooved ledge on which the black board rests; the pupils write down results in the ordinary notation and are led to the following conclusions :

(1) In a row of figures of the same kind each is worth ten times the one on the right and one-tenth of the one on the left.

(2) To multiply (or divide) by 10,100, . .. move all the figures one, two, places up-to the left (or down to the right), and fill up empty places with ciphers.

(3) Ciphers are used to represent empty places.

For preparation whole numbers are given to be multiplied and divided by powers of ten, and the pupils are told to write the figures on strips of paper and slip them backwards and forwards in named columns. (Possibly it would be useless to set such work for boys !

In the second lesson the ruling of the decimal columns is postponed till a division sum, with a power of ten for divisor, has shown the necessity for them. The result of this sum when written down makes it evident that the unit-place must be marked in some new way, hence the decimal point, which may be defined as the starting point for the decimals. A consideration of the method of multiplying two large numbers shows that empty places need not always be represented by

Teachers' Notes on English History. Would you kindly give in the correspondence column of The School World the name of the publisher and the price of Prof. Tout's “Analysis of English History,” recommended in the notes on “Oxford History ?”

T. SMITH. New Cross, S.E.

Prof. Tour's “ Analysis of English History," recommended in the Teachers' Notes, of which I am part author, is published by Messrs. Macmillan, is. ; but I should like to say, in general, that such information is supplied, with regard to many of the most useful historical works, in the article by Mr. Johnson Evans and myself, entitled, “ A Teacher's Library of English History," which appeared in the September, 1899, issue of The SCHOOL World. May I refer new subscribers to this magazine to that article for general information about books relating to English history?

May I add a request of my own? One or two writers in noneducaticnal papers have been pleased to regard my suggestions as to the use of historical novels (THE SCHOOL WORLI), vol. ii., p. 407) as a more or less diabolical plot for “disturbing the peace of a boy's playtime." I should be pleased to hear the opinion of readers of The School World as to whether they consider it either wicked or impossible to attempt to influence the pleasure-reading of their charges out of school hours and to

true.

concentrate it, as far as possible, on the work which is being done in school. I rejoice to find that I have a fellow."plotter” in one of Mr. Findlay's staff at Cardiff-Mr. N. L. Frazer, whose article on the subject in the Educational Review (December ist) I should like to commend to the notice of the readers of this magazine.

C. S. FEARENSIDE. Tenison Avenue, Cambridge.

Corporate Life in Public Day-Schools. MR. MUNRO's letter on “Corporate Life in Public Day. Schools” in your December issue deserves more serious consideration than I am able at the end of term to give to it, but I do not like to lose the opportunity of making one or two remarks. I was particularly struck by his insistence on the importance of preparation for municipal and local public life. Teachers in day-schools are in some danger of megalomania, and in their admiration for the " great public school” may aspire to training their pupils to be makers and rulers of the Empire. Such careers will probably in the future, as in the past, belong mainly to the rich, the gentry and the aristocracy. But through our day-schools pass those who will be guardians, members of school boards and technical committees, and of county councils; and the corporate life of a good school, together with the intellectual training of the class-room, should help to make them worthy rulers of country and town.

Mr. Munro is evidently aware how vain is the attempt to work up a good esprit before you have got your corps, and he makes a number of valuable suggestions for developing cor. porate lise in a class. Does he lay sufficient stress on eating and drinking ? Banquets or modest teas help to foster an esprit de classe. The difficulties may, in some cases, be inseparable, but in at least one London school--a school in the East Endit is found possible for the different forms to invite each other to tea in a room on the school premises, and the results are said to be admirable.

F. P. B. SHIPHAM. St. Olave's and St. Saviour's Grammar School,

Southwark. December 17th, 1900.

(2) The star makes its first appearance on the left of the figure. Looking towards the pole, the apparent motion is in the opposite direction to that of the hands of a watch, and as the star is crossing the meridian between the pole and the north point, the motion is from left to right.

(3) The window is carried round in front of the star by the rotation of the earth.

(4) There is no means of telling from the given track how long the star would be in traversing it. It is a portion of an ellipse, and gives no clue to the radius of the corresponding circle. [This is due to a slight fault in the drawing. The curve should have been an arc of a circle, but is not exactly

Assuming it to have been correctly drawn, the time occupied would have been about 2 hrs. - Editors SCHOOL WORLD.] Any star travelling over the same track would occupy the same time in crossing. A star above that track would take a longer time, whilst one below would take less. Those stars above the track, being nearer to the pole, appear to move in less circles, and a greater proportion is cut off by the window frame and vice versa. The same proportion of all circles is, however, passed over in the same time by the stars traversing them, and consequently those nearest the pole will keep in view for the longer times.

(5) The star will be in the same position again in 24 hours star time, or about 23 hours 56 minutes of mean solar (Greenwich) time. Star time differs from mean solar time by about four minutes a day. A day by star time is less by that amount than a mean solar day. The difference is due to the revolution of the earth round the sun, by which we get one star day more in a year than solar days. Astronomers use star time in most calculations, since the star is always in the same position at the same time by such a clock as keeps star time. As will be seen by the foregoing, this is not the case when mean solar time is used.

(6) This star could not be the Pole Star, for that star has such a small track as to be unnoticed without the aid of a telescope. The star is below the Pole Star. In order to make calculations the horizon should be observed on the same diagram, and then by measuring the distance from the eye to the window, the angle subtended by the line drawn at right angles to the horizon line from the lower position of the star can easily be determined. The difference between 511° and this angle is the distance from the pole.

(7) A star track will be straight is the star observed is on the celestial equator.

(8) A star is sun, though not necessarily in the same state as our own sun, many of them being at considerably higher temperatures.

(9) Stars shine in the day-time, but the very great brilliancy of the sun makes them invisible.

(10) Such stars as indicated never appear as shooting stars. They are, in general, enormous masses, greater than the sun, whilst falling stars rarely weigh more than a few pounds.

(11) The star would not be visible six months hence from the same window at the same time. It would be crossing the meridian between the pole and the south point and would appear to be exactly on the opposite side of the line joining the observer to the pole. This arises from the difference of times mentioned in (5)

(12) Neither the sun nor the moon could ever appear to follow this track, as in this latitude they never appear in the north. No meteor could follow it. The tracks of these bodies may be in any directions, and are independent of the earth's motion, which causes the apparent track shown. A comet could follow this track fairly closely, since the greater part of its apparently diurnal motion is due to the real motion of the earth.

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PRIZE COMPETITION.

Result of No. 12. It was scarcely expected that the “ Problem in Observational Astronomy” set as the subject of Competition No. 12 would bring many replies, for there were a number of questions to be answered, and the time was limited. Several more or less satisfactory papers have, however, been received, and from them we select the one printed below, by

Mr. L. Bairstow,
54, Redcliffe Road,

London, S.W., as the best. Two other papers worthy of especial mention are by Miss Helen Andrews, Friends' School, The Mount, York ; and Mr. T. L. Humberstone, the Grammar School, Market Bosworth. We intentionally did not put any age limit upon this competition, or make any stipulation that the answers should be written without the aid of books. The questions could only be satisfactorily answered by students who have watched the apparent movements of the stars themselves, and very little assistance could be obtained from books.

PRIZE ANSWERS. (1) The window faces north, due north being about onethird from the right. The star is just passing the meridian, as is seen from its reaching its lowest position. Had it been south the curve would have been convex upwards and not concave as shown.

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